The main objective of this question is to find the complement measure for the given statement.
This question uses the concept of complementary angle and complement measure. Two angles are said to be complementary if their sum results in 90 degrees, and for complement measure we have this formula:
90 – x
Expert Answer
We have to find the complement measure, which is mathematically equal to:
\[90 \space – \space x \]
From the given statement, we know that:
\[x \space = \space 5 (90 \space – \space x ) \space – \space 6 \]
We have to solve it for $ x $, results in:
\[x \space = \space 450 \space – \space 5 x \space – \space 6 \]
Subtracting $ 6 $ from $ 450 $results in:
\[x \space = \space 444 \space – \space 5 x \]
Adding $ 5x $ to both sides results in:
\[6x \space = \space 444 \]
Dividing by $ 6 $ on both sides results in:
\[x \space = \space 74 \]
Now we know that the complement measure is:
\[90 \space – \space x \]
So:
\[= \space 90 \space – \space 74 \]
\[= \space 16 ^ {\circ} \].
Numerical Answer
The complement measure for the given statement is $ 16 ^ {\circ} $.
Example
Determine the complement measure so the measure angle becomes 8 less and 10 less than six times of its complement.
We have to find the complement measure which is mathematically equal to:
\[90 \space – \space x \]
From the given statement, we know that:
\[x \space = \space 6 (90 \space – \space x ) \space – \space 8 \]
We have to solve it for $ x $, resulting in:
\[x \space = \space 540 \space – \space 6 x \space – \space 8 \]
Subtracting $ 8 $ from $ 540 $results in:
\[x \space = \space 532 \space – \space 6 x \]
Adding $ 6x $ to both sides results in:
\[7x \space = \space 532 \]
Dividing by $ 7 $ on both sides results in:
\[x \space = \space 76 \]
Now we know that the complement measure is:
\[90 \space – \space x \]
So:
\[= \space 90 \space – \space 76 \]
\[= \space 14 ^ {\circ} \].
Now:
We have to find the complement measure, which is mathematically equal to:
\[90 \space – \space x \]
From the given statement, we know that:
\[x \space = \space 6 (90 \space – \space x ) \space – \space 10 \]
We have to solve it for $ x $, resulting in:
\[x \space = \space 540 \space – \space 6 x \space – \space 10 \]
Subtracting $ 8 $ from $ 540 $results in:
\[x \space = \space 530 \space – \space 6 x \]
Adding $ 6x $ to both sides results in:
\[7x \space = \space 530 \]
Dividing by $ 7 $ on both sides results in:
\[x \space = \space 75.71 \]
Now we know that the complement measure is:
\[90 \space – \space x \]
So:
\[= \space 90 \space – \space 75.71 \]
\[= \space 14.29 ^ {\circ} \].